A.P. Physics – C

Unit 9: Magnetism

Unit 9 Study Guide * In studying for your test, make sure to study this review sheet along with your quizzes, labs, multiple choice practice, and homework assignments.

1. An electron is in a uniform magnetic field B that is directed into the plane of the page, as shown. When the electron is moving in the plane of the page in the direction indicated by the arrow, the force on the electron is directed… (A) (B) (C) (D) (E)

toward the right. toward the left. out of the page. toward the top of the page. toward the bottom of the page.

x x

e

x

x

x

x

x

x

x

x

x

x

Bin

2. The force between two current–carrying parallel wires is given by F. What is the resulting force if both currents are doubled, and the separation distance between the wires is also doubled? (A) F/4

3.

(B) F/2

(C) F

(D) 2F

(E) 4F

Use the right-hand rule to determine the direction of B, caused by I in the wire, at point P. (A) (B) (C) (D) (E)

Out of the page. Into the page. To the right. At 30o above the positive x-axis. At 60o below the positive x-axis.

I P



30o

4. A rectangular wire loop is at rest in a uniform magnetic field B of magnitude 2T that is directed into the page. The loop measures 5cm by 8cm, and the plane of the loop is perpendicular to the field, as shown. The total magnetic flux through the loop is (A) (B) (C) (D) (E)

zero 0.002 Wb 0.008 Wb 0.2 Wb 0.8 Wb

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

Bin

5.

An electron moving with a speed of 2x106 m/s perpendicular to a uniform magnetic field of 10-3 T will execute one revolution of a circular path in a time nearest to which one of the following? (B) 10-6 s

(A) 1 s

(C) 10-8 s

(D) 10-10 s

(E) 10-15 s

6. A positive charge q is moving with velocity v perpendicular to a magnetic field B shown into the paper in the figure. What are the magnitude and direction of the electric field that will allow the charge to pass undeflected? Magnitude (A) qvB

Direction left

(B)

B/v

left

(C)

Bv

right

(D)

Bv

left

(E)

Bv

out of paper

x

x

x

x

x

x

x

v q

Bin

x

x

x

x

x

7. Two singly-charged particles are shot with the same velocity into a uniform magnetic field (so that they are moving perpendicular to the field), and it is found that the particles both move in clockwise circular paths of different radii. Which of the following must be true of the two particles. (A) (B) (C) (D) (E)

8.

The particles have the same charge sign but different masses. The particles have the same charge sign and the same mass. The particles have different charge signs and different masses. The particles have different charge signs but the same mass. Both particles must be neutrally-charged and massless.

A current I, uniformly distributed over the cross section of a long cylindrical conductor of radius a, is directed as shown in the diagram. Which of the following graphs best represents the intensity B of the magnetic field as a function of the distance r from the axis of the cylinder? B

(A) O

(B) a

r

B

(D)

O

B

B

(E)

a

r

r

O

a

r

I

B

(C) a

O

a

O

a

r

9. Find the magnetic force, measured in Newtons, acting on a positive charge Q, moving through a magnetic field given by (3î+4ĵ)T, at a velocity of (2î+4ĵ)m/s. (A) 4Q kˆ

(B) -4Q kˆ

(C) 2Q kˆ

(D) -2Q kˆ

(E) 6Q kˆ

10. In what direction is the net force acting on the rectangular current-carrying loop in the diagram? (A) (B) (C) (D) (E)

To the right. To the left. Up the page. Down the page. Into the page.

I I

11. A long straight wire carries a current such that the strength of the magnetic field at a distance D from the wire is equal to B. What is the magnetic field strength at a distance of 2D from the wire? (A) B/4

(B) B/2

(C) B

(D) 2B

(E) 4B

12. A wire loop of radius r is inside an N-turn solenoid of radius R and length L, oriented perpendicular to the solenoid’s B- field. If the current in the solenoid changes at the constant rate of dI/dt, what emf is induced in the loop? (A) (B) (C) (D) (E)

zero (µoN)(dI/dt) (µoN/L)(dI/dt) (µoNπr2/L)(dI/dt) (µoNIπR2/L)(dI/dt)

13. Two conducting wire loops move near a very long, straight conducting wire that carries a current I. When the loops are in the positions shown, they are moving in the directions shown with the same constant speed v. Assume that the loops are far enough apart that they do not affect each other. Which of the following is true about the directions of the induced electric currents, if any, in the loops? (A) (B) (C) (D) (E)

Loop 1 No current No current Clockwise Clockwise Counterclockwise

Loop 2 No current Counterclockwise No current Clockwise No current

v

Loop 2

Loop 1 I

v

I (into page)

14. A cross section of a long solenoid that carries current I is shown to the right. All of the following statements about the magnetic field B inside the solenoid are correct EXCEPT:

I (out of page)

Axis

(A) B is directly to the left. (B) An approximate value for the magnitude of B may be determined by using Ampere’s law. (C) The magnitude of B is proportional to the current I. (D) The magnitude of B is proportional to the number of turns of wire per unit length. (E) The magnitude of B is proportional to the distance from the axis of the solenoid.

15. A loop of wire is at rest in a magnetic field, as shown. If the strength of the field is increased, in what direction will current be induced in the loop? (A) (B) (C) (D) (E)

Into the page. Out of the page. Clockwise around the loop. Counterclockwise around the loop. No current is induced.

x

x

x

x

x

x

x

x

x

x

x

x

Bin

16. A positive charge initially has an angled velocity in the x-y plane, as shown in the diagram, when the particle enters a region of space where a uniform magnetic field exists, directed along the + x-axis. The subsequent motion of the charge could best be described as… (A) (B) (C) (D) (E)

circular motion in the x-y plane. uniform motion. circular motion in the x-z plane. helical motion with axis parallel to the x-axis. helical motion with axis parallel to the y-axis.

v

B

+

17. A magnetic field perpendicular to the plane of a wire loop is uniform in space but changes in time, according to the function B=at-b, where a and b are positive constants. Which of the following correctly describes the induced emf in the wire loop, as time goes on? (A) (B) (C) (D) (E)

zero Constant in magnitude Increasing in magnitude Decreasing in magnitude This question cannot be answered without knowing the values of a and b.

18. An electron is accelerated through a potential difference of 20V before it enters perpendicularly into a magnetic field of strength 0.03T. Determine the magnitude and direction of the magnetic force that acts on the electron, assuming it moves in the positive y-direction and the B-field is directed along the negative x-axis.

19.

20.

A proton moving with velocity given by (3î – 4ĵ)m/s moves through a magnetic field given

by 0.2 kˆ T. In unit vector notation, what is the magnetic force experienced by the proton?

A charged particle with mass of 4.5x10-15 kg and charge of +8.2x10-16 C moves at 1.5x104 m/s in the positive x-direction through a 34,000N/C electric field directed in the positive y-direction. Find the magnitude and direction of the magnetic field that must exist in this same region of space, for the particle to move in a straight-line path through both fields.

21.

An electron with kinetic energy of 80eV moves in a circular path in a uniform magnetic field. If the radius of the electron’s path is 24cm, calculate… a. the strength of the magnetic field.

b.

22.

the frequency of the electron’s circular motion.

Two long straight wires are 4cm apart, and carry 0.3A currents into and out of the page, as shown in the diagram. a. Calculate the net magnetic field at point P, located on a perpendicular bisector to the wires.

P

7cm

X 4cm

b. Calculate the magnitude and direction of the magnetic force per unit length acting on the rightmost wire, due to the field created by the other wire.

23.

Four wires carry currents into and out of the page as shown. Calculate

  the value of the line integral ∫ B ⋅ d  for the path indicated.

X

4A

2A

X

3A 1.5A

24.

A long, cylindrical wire of radius 4.2mm carries a uniform current of 0.13A. Use Ampere’s law to calculate the magnitude of the magnetic field… a. at a point 5.6mm from the wire’s central axis.

b. at a point 3.5mm from the wire’s central axis.

25.

A solenoid of length L and radius R has N total turns along its length, and carries a current I. a. Use Ampere’s law to derive an expression for the strength of the magnetic field B inside the solenoid.

b. Now if L=25cm and N=300 turns, calculate the value of I in order for B to equal 0.2T inside the solenoid.

26. A piece of wire with a resistivity of 1.5x10-8 Ωm and cross-sectional radius of 5.1mm is bent into a 20-turn circular coil with a radius of 12cm. The coil is placed in an external magnetic field of strength 0.25T with the plane of the coil perpendicular to the field direction. If the field strength increases at a rate of 0.04T/s, calculate the current that is induced in the coil.

27. A flexible coil of wire has an area that changes according to A(t) = 4t2 - 3t. If this flat coil is oriented horizontally, and placed in a 7.4mT uniform magnetic field directed at an angle of 40o from the vertical, calculate the magnitude of emf induced in the coil at t=57ms.

28. A long, straight wire carries a current of 45mA, as shown, and a rectangular loop with dimensions of 3cm by 5 cm rests below the wire, in the same plane as the wire. If the top edge of the loop is 4cm below the wire, calculate the magnetic flux through the loop. I

29. Actual A.P. Physics C Free-Response Question, sort of (1993): L V

y

d

B K

R z

x

(Positive z out of the page)

A mass spectrometer, constructed as shown in the diagram, is to be used for determining the mass of singly ionized positively charged ions. There is a uniform magnetic field B = 0.02T, perpendicular to the page in the shaded region of the diagram. A potential difference V = 1,500 volts is applied across the parallel plates L and K, which are separated by a distance d = 0.012 meters and which act as a velocity selector. (a) In which direction, relative to the coordinate system shown above on the right, should the magnetic field point in order for positive ions to move along the path shown by the dashed line in the diagram? (b) In what direction, relative to the coordinate system shown above on the right, should the electric field between the plates point in order for positive ions to move along the path shown by the dashed line in the diagram? (c) Calculate the magnitude of the electric field between the plates.

(d) Calculate the speed of a particle that can pass between the parallel plates without being deflected.

(e) Calculate the mass of a hypothetical singly charged ion that travels in a semicircle of radius R = 0.50 meter.

(f) A doubly ionized positive ion of the same mass and velocity as the singly charged ion enters the mass spectrometer. What is the radius of its path?

30. Actual A.P. Physics C Free-Response Question, sort of (2007):

In the diagram above, a nichrome wire of resistance per unit length λ is bent at points P and Q to form horizontal conducting rails that are a distance L apart. The wire is placed within a uniform magnetic field of magnitude B that is pointing into the page. A conducting rod of negligible resistance, which was aligned with end PQ at time t=0, slides to the right with constant speed v and negligible friction. Express all algebraic answers in terms of the given quantities and fundamental constants. (a) Indicate the direction of the current induced in the circuit. _____Clockwise _____Counterclockwise Justify your answer. (b) Derive an expression for the magnitude of the induced current as a function of time t.

(c) Derive an expression for the magnitude of the magnetic force on the rod as a function of time.

(d) On the given axes, sketch a graph of the external force Fext as a function of time that must be applied to the rod to keep it moving at constant speed while in the field. Label the values of any intercepts.

31. Actual A.P. Physics C Free-Response Question (2013): The figure to the right shows a circular loop of area 0.25 m and resistance 12 Ω that lies in the plane of the page. A magnetic field of magnitude B directed into the page exists in the area of the loop. The field varies with time t, as shown in the graph below.

(a)

i.

Derive an expression for the magnitude of the induced emf in the loop as a function of time for the interval t = 0 s to t = 8 s.

ii. Calculate the magnitude of the induced current I in the loop at time t = 4 s.

(b)

i. Sketch a graph of the induced current I in the loop as a function of time t from t = 0 s to t = 18 s on the axes below, assuming that a counterclockwise (CCW) current is positive.

ii. For the time interval 12 s to 16 s, justify the direction of the current you have indicated in your graph.

(c) Calculate the total energy dissipated in the loop during the first 8 s shown.

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